Finite Group Databasebeta

← #11786428

Subgroups — #11786428

Order 1152.

562 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C2×#63769C212yesmaximal, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic
5#10590182C212yesmaximal, complemented
6C23×#157—21no—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×C4⋊#157—24no—
11C2×C4⋊#157C2211yescharacteristic
12C2×C4⋊#157C2211yescharacteristic
13C2×C4⋊#157C2212yes—
14C2×C8×C3⋊D3C2212yes—
15#63781—21no—
16#63769—24no—
17C32×C22⋊C8C411yescharacteristic, complemented
18#63657C411yescharacteristic, complemented
19#63647C412yescomplemented
20D3×C22⋊C8—62no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—24no—
23C22×#157—22no—
24C22×#157—21no—
25C22×#157—21no—
26C22×#157—42no—
27C22×#157—42no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3Q811yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3Q811yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C22⋊#157—42no—
37C4⋊#157—24no—
38C4⋊#157—22no—
39C4⋊#157—22no—
40C4⋊#157—22no—
41C4⋊#157D414yes—
42C2×C32×C8C2×C412yescomplemented
43C2×C3⋊(C3⋊C8)C2×C412yescomplemented
44C8×C3⋊D3—22no—
45C8×C3⋊D3—22no—
46#1852—91nomaximal, Sylow
47C22×C4×D3—62no—
48C2×D3×C8—64no—
49C3×C22⋊C8—22no—
50#830—62no—
51(C2×D3)⋊C8—64no—
52C23×C32C4⋊C411yescharacteristic
53C22×C3⋊D3—21no—
54C22×C3⋊D3—21no—
55C22×C3⋊D3—21no—
56C22×C3⋊D3—21no—
57C22×C3⋊D3C4⋊C411yescharacteristic
58C22×C3⋊D3D812yes—
59C22×C3⋊D3Q1612yes—
60C22×C3⋊D3C2×D411yescharacteristic
61C2×#157—24no—
62C2×#157—48no—
63C2×#157—42no—
64C2×#157—42no—
65C2×#157—41no—
66C2×#157—41no—
67C2×#157—41no—
68C2×#157—41no—
69C2×#157—41no—
70C2×#157—41no—
71C2×C32×C4—22no—
72C2×C32×C4C4⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3C4⋊C411yescharacteristic
76C2×C3⋊Dic3C2×Q811yescharacteristic
77C4×C3⋊D3—21no—
78C4×C3⋊D3—21no—
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3C2×D412yes—
82C4×C3⋊D3#4112yes—
83C32×C8—22no—
84C3⋊(C3⋊C8)—22no—
85C22×C4⋊C4—91no—
86C2×#107—92no—
87C2×C22⋊C8—91no—
88#380—91no—
89#340—92no—
90C23×D3—62no—
91C22×C3×C4—22no—
92C22×Dic3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—124no—
98C2×C4×D3—124no—
99C2×C3×C8—24no—
100C2×C3⋊C8—64no—
101D3×C8—124no—
102D3×C8—124no—
103C22×C32—21no—
104C22×C32—21no—
105C22×C32#10712yescomplemented
106C22×C32C2×C4⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—22no—
113C2×C3⋊D3#10712yescomplemented
114C2×C3⋊D3#12011yescharacteristic
115C2×C3⋊D3#12311yescharacteristic
116C2×C3⋊D3C2×D811yescharacteristic
117C2×C3⋊D3C2×Q1611yescharacteristic
118C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
119C2×C3⋊D3#13711yescharacteristic
120#157—44no—
121#157—81no—
122#157—81no—
123C32×C4—21no—
124C32×C4C4×D412yes—
125C3⋊Dic3—21no—
126C3⋊Dic3C22⋊Q812yes—
127C23×C4—91no—
128C23×C4—181no—
129C22×C8—92no—
130C2×C4⋊C4—92no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—91no—
133C2×C4⋊C4—184no—
134C2×C4⋊C4—181no—
135C2×C22⋊C4—181no—
136#107—184no—
137C22⋊C8—91no—
138C22⋊C8—92no—
139C22⋊C8#15711yescharacteristic, complemented
140#95—181no—
141C23×C3—22no—
142C22×D3—62no—
143C22×D3—62no—
144C22×D3—64no—
145C22×D3—64no—
146C22×D3—122no—
147C22×D3—122no—
148C22×D3—122no—
149C22×D3—122no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—44no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—124no—
156C4×D3—64no—
157C4×D3—64no—
158C4×D3—124no—
159C4×D3—124no—
160C4×D3—122no—
161C4×D3—122no—
162C3×C8—44no—
163C3⋊C8—124no—
164C2×C32—22no—
165C2×C32#38511yescharacteristic
166C2×C32C2×#10711yescharacteristic
167C2×C32#42811yescharacteristic
168C3⋊D3—22no—
169C3⋊D3#44711yescharacteristic
170C3⋊D3#45111yescharacteristic
171C3⋊D3#48011yescharacteristic
172C3⋊D3#48411yescharacteristic
173C24—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—182no—
180C22×C4—182no—
181C22×C4—182no—
182C22×C4—184no—
183C22×C4—181no—
184C22×C4—181no—
185C22×C4—362no—
186C22×C4—362no—
187C22×C4C2×#15711yescharacteristic
188C2×C8—92no—
189C2×C8—182no—
190C2×C8—182no—
191C2×C8C2×#15712yescomplemented
192C4⋊C4—94no—
193C4⋊C4—182no—
194C4⋊C4—182no—
195C4⋊C4—182no—
196C4⋊C4—184no—
197C22⋊C4—362no—
198C22×C3—24no—
199C22×C3—22no—
200C22×C3—42no—
201C22×C3—42no—
202C2×D3—62no—
203C2×D3—62no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—62no—
208C2×D3—64no—
209C2×D3—124no—
210C2×D3—124no—
211C2×D3—124no—
212C2×D3—124no—
213C2×D3—122no—
214C2×D3—122no—
215C3×C4—24no—
216C3×C4—42no—
217Dic3—64no—
218Dic3—122no—
219C32#185211yescharacteristic, complemented, Sylow
220C23—91no—
221C23—92no—
222C23—92no—
223C23—91no—
224C23—181no—
225C23—181no—
226C23—181no—
227C23—181no—
228C23C4⋊#15711yescharacteristic
229C2×C4—22no—
230C2×C4—91no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—91no—
234C2×C4—182no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—184no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4—368no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4C4⋊#15711yescharacteristic
250C2×C4C22×#15711yescharacteristic
251C8—22no—
252C8—182no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—44no—
257D3—62no—
258D3—62no—
259D3—62no—
260D3—62no—
261D3—124no—
262C22—21no—
263C22—21no—
264C22—91no—
265C22—91no—
266C22—91no—
267C22—91no—
268C22—91no—
269C22—91no—
270C22—92no—
271C22—182no—
272C22—182no—
273C22—182no—
274C22—182no—
275C22—181no—
276C22—181no—
277C22#6376912yescomplemented
278C22C2×C4⋊#15711yescharacteristic
279C4—21no—
280C4—92no—
281C4—181no—
282C4—364no—
283C4—721no—
284C4—721no—
285C4D4×#15712yes—
286C3—22no—
287C2—22no—
288C2—91no—
289C2—91no—
290C2—91no—
291C2—91no—
292C2—182no—
293C2#1059374611yescharacteristic
294C2C2×#6376911yescharacteristic
295C2#1059377411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊C8#157
hypocenterC32#1852
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#63769C2semidirect
5. #10590182C2semidirect
17. C32×C22⋊C8C4semidirect
18. #63657C4semidirect
19. #63647C4semidirect
42. C2×C32×C8C2×C4semidirect
43. C2×C3⋊(C3⋊C8)C2×C4semidirect
105. C22×C32#107semidirect
113. C2×C3⋊D3#107semidirect
139. C22⋊C8#157semidirect
191. C2×C8C2×#157semidirect
219. C32#1852semidirect
277. C22#63769semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4⋊#1572
#105938122
C2×#637692
C3⋊D3×C22⋊C82
#105901822
#18529